(CRM-, Joint-) Colloquium

Supported by

Coffee: Common Room, before the colloquium at 3pm.

Speaker: Andrei Rapinchuk (Virginia)
Title: Number-theoretic techniques in the theory of Lie groups and differential geometry
Abstract: I will give an overview of the ongoing joint work with Gopal Prasad on length-commensurable and isospectral locally symmetric spaces. The centerpiece of this work is the new notion of weak commensurability for Zariski-dense subgroups. We have been able to determine when two arithmetic subgroups are weakly commensurable. This leads to various geometric results, some of which are related to the famous question ``Can one hear the shape of a drum?" Home-page

Speaker: Sergey Bezuglyi (Insitute for Low Temperature Physics, Kharkov, Ukraine)
Title: Homeomorphic finite and infinite measures on a Cantor set
Abstract: Two measures, m and m' on a topological space X are called homeomorphic if there is a homeomorphism f of X such that m(f(A)) = m'(A) for any Borel set A. The question when two Borel probability non-atomic measures are homeomorphic has a long history. The well-known result of Oxtoby and Ulam gives a criterion when a probability Borel measure on the cube [0, 1]^n is homeomorphic to the Lebesgue measure. The situation is more difficult for measures on a Cantor set. There is no complete answer to the above question even in the simplest case of Bernoulli trail measures. In my talk, I will first discuss some relatively recent results about classification of Bernoulli measures proved by Akin, Dougherty, Mauldin, Yingst. Then these ideas will be used to study finite and infinite measures on a Cantor set up to a homeomorphism. I will focus on the case of invariant (finite or infinite) ergodic measures for aperiodic substitutions.

Speaker: Ivan Dimitrov (Queens)
Title: Inversion sets of permutations
Abstract: If s is a permutation of {1, 2, ... , n} then an inversion of s is a pair i < j with s(i) > s(j). In this talk I will describe all triples s_1, s_2, s_3 such that the inversion set of s_3 equals the disjoint union of the inversion sets of s_1 and s_2. This elementary combinatorial problem has a beautiful solution and is related to problems ranging from combinatorics to geometry. I will explain some of these relationships and will present some experimental numerical data.
This work is the outcome of a couple of NSERC USRA projects and is joint with Rian Dewji, Adam McCabe, Mike Roth, David Wehlau, and Jennifer Wilson.

Speaker: Albert Meads Fisher (Sao Paulo, Brazil)
Title: Small- (and large-) scale stucture via flows
Abstract: We study the small scale of geometric objects embedded in a Euclidean space by means of the flow defined by zooming toward a point in the object. For Fuchsian and Kleinian limit sets this 'scenery flow' corresponds naturally to the geodesic flow, and one has in both cases the formula 'scenery flow entropy equals Hausdorff dimension of limit set', unifying dimension formulas of Sullivan for the Kleinian case and of Bowen-Ruelle for hyperbolic Julia sets. We explore this analogy in a variety of examples, some related to adic transformations and some to stable and to renewal processes. This includes joint work with Pierre Arnoux and Marina Talet.

Speaker: N. Balakrishnan (McMaster)
Title: Cure Rate Models and Associated Inference
Abstract: In this talk, I will first introduce two classical cure rate models and then describe how more flexible models can be obtained. These models would allow for over- and under-dispersion as well, in comparison to the well-known Poisson cure rate model. I shall then detail some inferential aspects associated with this general cure rate model and illustrate it by fitting to a cutaneous melanoma data. Finally, I will mention some other variations that could be made to the model based on some biological considerations and associated inferential results.
Short Bio: Dr. Balakrishnan is a professor in the Department of Mathematics and Statistics at McMaster University. Originally from India, he obtained his B.Sc. and M.Sc from the University of Madras and a PhD from The Indian Institute of Technology in Kanpur in 1981. Just after finishing his PhD, Dr. Balakrishnan came to Canada and held positions in different Canadian Universities and then in 1986 he joined the faculty at McMaster as an assistant professor. In 1995, he became a full professor. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute. He has held Distinguished Eugene Lukcas Professorship at Bowling Green State University (Ohio) and Santalo Lecturership at Universidad Complutense (Madrid, Spain).

Speaker: Jason Brown (Dalhousie)
Title: The Mathematics Underlying Musical Mysteries
Abstract: Mathematics is the science of patterns, and patterns infuse music. Mathematics allows us to understand the aesthetics of music, that go on at both a conscious and subconscious level. In this talk we'll apply a variety of mathematics to discover why we love music the way we do, and to uncover mysteries hidden in the best of pop music.
Shor Bio: Jason I. Brown received a Ph.D. in mathematics from the University of Toronto in 1987 and is currently a professor of Mathematics at Dalhousie University in Halifax, Nova Scotia. He has written over 60 refereed research papers in combinatorics and its connections to other branches of mathematics. He employed mathematical research to uncover how The Beatles played the opening chord of A Hard Day's Night in 2004 and garnered widespread media attention, and his work has been featured on the front page of the National Post, in Guitar Player magazine and on the web site of the Wall Street Journal. He is also the author of "Our Days Are Numbered: How Mathematics Orders Our LIves".